Questions and Answers
If $\Delta ABC \cong \Delta DEF$, which of the following statements is true?
All of the above
In the given figure, if $\Delta ACT \cong \Delta SHE$, what is the value of $x$?
50
If $LM \cong ZR$, which congruence postulate can be used to prove that $\Delta NIM \cong \Delta ZER$?
Side-Side-Side (SSS) Congruence Postulate
If $\Delta ACT \cong \Delta SHE$, and $AC = 6$ cm, what is the length of $SH$?
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Which of the following pairs of triangles appear to be congruent in the given figure?
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Which theorem is best illustrated by two triangles that have two pairs of congruent corresponding sides and one pair of congruent corresponding angles?
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If two triangles are congruent by the Side-Angle-Side (SAS) Congruence Theorem, what additional information is needed to prove congruence?
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Which congruence theorem can be used to prove two triangles are congruent if all three sides of one triangle are congruent to the corresponding sides of the other triangle?
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If two triangles have two pairs of congruent corresponding angles and one pair of congruent corresponding sides, which congruence theorem can be used to prove the triangles are congruent?
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If two triangles are congruent by the Side-Side-Side (SSS) Congruence Theorem, what additional information is needed to prove congruence?
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Which of the following is NOT a valid congruence theorem for proving two triangles are congruent?
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Study Notes
Congruent Triangles
- When assigning points on a truss, we need to identify pairs of triangles that appear to be congruent.
- Basis for choosing pairs of triangles: congruent triangles have the same shape and size.
Solving Corresponding Parts of Congruent Triangles
- When two triangles are congruent, their corresponding parts are equal.
- Example: ∆NIM and ∆ZER have 6 pairs of corresponding parts.
Practice Exercises
- Example 5: identify congruent triangles, write statement of correspondence, and find measures.
- Example 6: identify congruent triangles, write statement of correspondence, and find measures.
Geometry in Daily Life
- Geometry has numerous practical applications in daily life.
- Example: identifying objects around us that illustrate different theorems (e.g. congruent triangles).
Performance Task
- Take a picture of an object or cut pictures from a magazine/newspaper that illustrates a theorem.
- Identify which specific part corresponds to the theorem and mark the congruent parts.
- Specify the theorem illustrated on the picture.
- Each picture properly labeled with correct theorem will be given 10 points.
Illustrating Triangle Congruence
- Directions: identify vertices, angles, and sides of each triangle.
- Given ∆DRY ≅ ∆SOT, identify corresponding parts congruent to each given side or angle.
Illustrating Congruence Postulates
- SAS, ASA, and SSS congruence postulates can be used to prove triangle congruence.
- Identify additional corresponding parts needed to make triangles congruent using specified congruence postulates.
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Description
This quiz discusses identifying congruent triangles in a truss structure, determining pairs of congruent triangles, and solving for corresponding parts of congruent triangles. Practice statements and measure calculations are included in the examples.
